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Modern blockchains face a scalability challenge due to the intrinsic throughput limitations of consensus protocols. Layer 2 optimistic rollups (L2) are a faster alternative that offer the same interface in terms of smart contract development and user interaction. Optimistic rollups perform most computations offchain and make light use of an underlying blockchain (L1) to guarantee correct behavior, implementing a cheaper blockchain on a blockchain solution. With optimistic rollups, a sequencer calculates offchain batches of L2 transactions and commits batches (compressed or hashed) to the L1 blockchain. The use of hashes requires a data service to translate hashes into their corresponding batches. Current L2 implementations consist of a centralized sequencer (central authority) and an optional data availability committee (DAC). In this paper, we propose a decentralized L2 optimistic rollup based on Setchain, a decentralized Byzantine-tolerant implementation of sets. The main contribution is a fully decentralized "arranger" where arrangers are a formal definition combining sequencers and DACs. We prove our implementation correct and show empirical evidence that our solution scales. A final contribution is a system of incentives (payments) for servers that implement the sequencer and data availability committee protocols correctly, and a fraud-proof mechanism to detect violations of the protocol.

Blockchains are decentralized systems that provide trustable execution guarantees. Smart contracts are programs written in specialized programming languages running on blockchains that govern how tokens and cryptocurrency are sent and received. Smart contracts can invoke other smart contracts during the execution of transactions always initiated by external users. Once deployed, smart contracts cannot be modified, so techniques like runtime verification are very appealing for improving their reliability. However, the conventional model of computation of smart contracts is transactional: once operations commit, their effects are permanent and cannot be undone. In this paper, we proposed the concept of future monitors which allows monitors to remain waiting for future transactions to occur before committing or aborting. This is inspired by optimistic rollups, which are modern blockchain implementations that increase efficiency (and reduce cost) by delaying transaction effects. We exploit this delay to propose a model of computation that allows (bounded) future monitors. We show our monitors correct respect of legacy transactions, how they implement future bounded monitors and how they guarantee progress. We illustrate the use of future bounded monitors to implement correctly multi-transaction flash loans.

Blockchain technologies are facing a scalability challenge, which must be overcome to guarantee a wider adoption of the technology. This scalability issue is due to the use of consensus algorithms to guarantee the total order of the chain of blocks and of the transactions within each block. However, total order is often not fully necessary, since important advanced applications of smart-contracts do not require a total order among all operations. A much higher scalability can potentially be achieved if a more relaxed order can be exploited. In this paper, we propose a novel distributed concurrent data type, called Setchain, which improves scalability significantly. A Setchain implements a grow-only set whose elements are not ordered, unlike conventional blockchain operations. When convenient, the Setchain allows forcing a synchronization barrier that assigns permanently an epoch number to a subset of the latest elements added, agreed by consensus. Therefore, two operations in the same epoch are not ordered, while two operations in different epochs are ordered by their respective epoch number. We present different Byzantine-tolerant implementations of Setchain, prove their correctness and report on an empirical evaluation of a prototype implementation. Our results show that Setchain is orders of magnitude faster than consensus-based ledgers, since it implements grow-only sets with epoch synchronization instead of total order. Since Setchain barriers can be synchronized with the underlying blockchain, Setchain objects can be used as a sidechain to implement many decentralized solutions with much faster operations than direct implementations on top of blockchains. Finally, we also present an algorithm that encompasses in a single process the combined behavior of Byzantine servers, which simplifies correctness proofs by encoding the general attacker in a concrete implementation., Comment: 32 pages 6 figures. arXiv admin note: substantial text overlap with arXiv:2206.11845

Blockchains are modern distributed systems that provide decentralized financial capabilities with trustable guarantees. Smart contracts are programs written in specialized programming languages running on a blockchain and govern how tokens and cryptocurrency are sent and received. Smart contracts can invoke other contracts during the execution of transactions initiated by external users. Once deployed, smart contracts cannot be modified and their pitfalls can cause malfunctions and losses, for example by attacks from malicious users. Runtime verification is a very appealing technique to improve the reliability of smart contracts. One approach consists of specifying undesired executions (never claims) and detecting violations of the specification on the fly. This can be done by extending smart contracts with additional instructions corresponding to monitor specified properties, resulting in an onchain monitoring approach. In this paper, we study transaction monitoring that consists of detecting violations of complete transaction executions and not of individual operations within transactions. Our main contributions are to show that transaction monitoring is not possible in most blockchains and propose different execution mechanisms that would enable transaction monitoring.

Blockchain technologies are facing a scalability challenge, which must be overcome to guarantee a wider adoption of the technology. This scalability issue is mostly caused by the use of consensus algorithms to guarantee the total order of the chain of blocks (and of the operations within each block). However, total order is often overkilling, since important advanced applications of smart-contracts do not require a total order of all the operations. Hence, if a more relaxed partial order (instead of a total order) is allowed under certain safety conditions, a much higher scalability can be achieved. In this paper, we propose a distributed concurrent data type, called Setchain, that allows implementing this partial order and increases significantly blockchain scalability. A Setchain implements a grow-only set object whose elements are not totally ordered, unlike conventional blockchain operations. When convenient, the Setchain allows forcing a synchronization barrier that assigns permanently an epoch number to a subset of the latest elements added. With the Setchain, operations in the same epoch are not ordered, while operations in different epochs are. We present different Byzantine-tolerant implementations of Setchain, prove their correctness and report on an empirical evaluation of a direct implementation. Our results show that Setchain is orders of magnitude faster than consensus-based ledgers to implement grow-only sets with epoch synchronization. Since the Setchain barriers can be synchronized with block consolidation, Setchain objects can be used as a sidechain to implement many smart contract solutions with much faster operations than on basic blockchains.

We consider minimum-cardinality Manhattan connected sets with arbitrary demands: Given a collection of points $P$ in the plane, together with a subset of pairs of points in $P$ (which we call demands), find a minimum-cardinality superset of $P$ such that every demand pair is connected by a path whose length is the $\ell_1$-distance of the pair. This problem is a variant of three well-studied problems that have arisen in computational geometry, data structures, and network design: (i) It is a node-cost variant of the classical Manhattan network problem, (ii) it is an extension of the binary search tree problem to arbitrary demands, and (iii) it is a special case of the directed Steiner forest problem. Since the problem inherits basic structural properties from the context of binary search trees, an $O(\log n)$-approximation is trivial. We show that the problem is NP-hard and present an $O(\sqrt{\log n})$-approximation algorithm. Moreover, we provide an $O(\log\log n)$-approximation algorithm for complete bipartite demands as well as improved results for unit-disk demands and several generalizations. Our results crucially rely on a new lower bound on the optimal cost that could potentially be useful in the context of BSTs.